However, for a large numbers of PDEs, such as the fundamental equations of fluid dynamics, the forward problem may not be well-posed. Existence, uniqueness or stability of solutions are either not true or not established rigorously. This issue is further exacerbated by the fact that for many of these PDEs, numerical approximations either may not converge on mesh refinement or converge too slowly to be useful. This is often a result of the sensitivity of solutions to small perturbations and the appearances of structures at smaller and smaller scales, as the grid is refined [1]}, [2]}, [3]}.
